A371424 Square array A(n, k), n, k > 0, read and filled in the greedy way by upward antidiagonals with distinct positive integers such that each term except A(1, 1) is a multiple of some earlier term on the same row or column.

1, 2, 3, 4, 6, 5, 7, 8, 10, 9, 11, 12, 15, 14, 13, 16, 18, 20, 24, 22, 17, 19, 21, 25, 27, 26, 28, 23, 29, 30, 32, 33, 35, 34, 36, 31, 37, 39, 38, 42, 44, 40, 45, 46, 41, 43, 48, 50, 54, 52, 51, 49, 56, 58, 47, 53, 57, 55, 63, 60, 64, 66, 62, 68, 70, 59

Offset

1,2

Comments

As a flat sequence, this is a permutation of the positive integers with inverse A371425 (as each row and column starts with the least missing value so far).

Empirically, for m > 1:

- the multiples of m appear along lines parallel to the borders and along two network of curves (see first illustration in Links section),

- the sequence mod m shows periodic patterns along the borders (see second illustration in Links section).

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10011

Rémy Sigrist, Scatterplot of (n, k) such that A(n, k) is a multiple of 7 and n, k <= 1000

Rémy Sigrist, Colored scatterplot of A(n, k) mod 7 for n, k <= 1000 (white pixels correspond to multiples of 7)

Rémy Sigrist, PARI program

Index entries for sequences that are permutations of the natural numbers

Example

Array A(n, k) begins:  n\k |  1   2   3    4    5    6    7    8    9   10   11   12
  ----+--------------------------------------------------------
    1 |  1   3   5    9   13   17   23   31   41   47   59   67
    2 |  2   6  10   14   22   28   36   46   58   70   74   94
    3 |  4   8  15   24   26   34   45   56   68   84   96  116
    4 |  7  12  20   27   35   40   49   62   77   91  112  119
    5 | 11  18  25   33   44   51   66   75   82   99  118  121
    6 | 16  21  32   42   52   64   80   92  105  126  144  160
    7 | 19  30  38   54   60   76   90  108  123  133  162  188
    8 | 29  39  50   63   78   87  100  124  145  156  174  200
    9 | 37  48  55   72   88  102  115  138  154  176  192  220
   10 | 43  57  65   86  104  114  135  155  171  195  215  232
   11 | 53  69  85   98  120  136  147  184  196  212  236  265
   12 | 61  81  95  117  130  152  180  183  210  235  260  285

Prog

(PARI) \\ See Links section.

Crossrefs

Cf. A371425 (inverse).

Sequence in context: A085175 A130111 A104182 * A371425 A361940 A361926

Adjacent sequences: A371421 A371422 A371423 * A371425 A371426 A371427

Keyword

nonn,tabl

Author

Rémy Sigrist, Mar 23 2024

Status

approved